# AUGUSTE BRAVAIS (1811 - 1863). *Mémoire sur les Systèmes Formeés par des Points Distribués Regulièerement sur un Plan or dans d'Espace* (*J. Ecole Polytech.* **1850**, *19*, 1-128.)

Bravais received a classical education at the Collè Stanislas in Paris, graduating in 1827. In 1829, he won first prize in mathematics in a general competition and was accepted to the École Polytechnique. He was first in his class at the end of the first year which made him eligible to select any technical field except mining. Since his passion from youth was to explore the world, he chose to enter the French navy. In 1832, Bravais sailed the Mediterranean and in April of that year was assigned to map the coast of Algeria. Several important publications on the structures and functions of plant organs, which stemmed from his travels, won him membership in the Société Philomathique de Paris in 1835. On an extended assignment in Norwegian Lapland from 1838 to 1839, he made numerous observations in astronomy, meteorology, and terrestrial magnetism.

Several years later, in 1845, Bravais accepted an appointment as professor of physics at the École Polytechnique. There, he became interested in symmetry, and sent several papers to the Académie de Sciences that were important in the development of modern crystallography. Specifically, he analyzed the types of geometric figures formed by points distributed regularly in space, and then applied these considerations to crystals. The points could be viewed as being the centers of gravity of the chemical molecules or as poles of forces.

Most important, Bravais demonstrated that there are fourteen space lattices, or regularly repeating arrangements of points in space, that differ in symmetry and geometry. He perceived that these fourteen space lattices exhibited seven different types of lattice symmetries, which corresponded to the previously recognized seven crystal systems. Hence, through Bravais's work the external symmetry of a crystal became firmly related toits internal symmetry, as embodied in the space lattice.

For more than 100 years, Bravais was given credit for first discovering the 14 crystal lattices, but relatively recent scientific scholarship revealed that his results were actually discovered twice before: first by Moritz Frankenheim in 1826 and again by Johann Hessell in 1830. Bravais deserves credit, however, for devising a rigorous proof of the result, and bringing it to the attention of the scientific community.

Curtis P. Schuh, *Mineralogy & Crystallography: An Annotated Bibliography of Books Published 1469 through 1919.* Tucson: privately published, 2005, p256-257.